German Patent Application No. 40 08 675 describes a conventional fuel injector including a valve needle, which in turn consists of an armature, a valve closing element, and a sleeve-shaped or tube-shaped connecting tube which connects the armature with the valve closing element, which can be spherical, for example. The parts listed represent individual parts which are manufactured separately, and which must be connected by means of joining methods which act on their substance, for example by means of laser-welding. Therefore there are at least two joints which result from the use of such joining methods. Because of the high thermal stress which occurs during methods such as welding or soldering, undesirable deformation of the valve needle can occur. The armature surrounds the connecting tube completely in the radial direction, and at least partially in the axial direction, since the connecting tube is attached in a lengthwise continuous aperture in the armature. The connecting tube itself also has an inner lengthwise continuous aperture, in which the fuel can flow in the direction of the valve closing element, and then exit close to the valve closing element, through crosswise apertures which are made in the wall of the connecting tube, and run radially.